The MTA is nearing completion on a $250 million anti-terror project to reinforce underwater subway tunnels and bridges against a bomb blast, The Post has learned.

Since 2004, agency contractors have been lining subway tubes — especially the 10 that run under the East River — with high-impact-bearing metal that would prevent collapse or massive flooding in the case of a terrorist attack, multiple sources said.

And in the more shallow tunnels that aren’t fully dug into rock, like the F line that connects 63rd Street to Roosevelt Island, workers dropped massive slabs of rock and concrete on the riverbed to prevent disaster, the sources said.

The Post revealed yesterday how the Port Authority is paying $600 million to beef up the vulnerable PATH subway tunnels beneath the Hudson River with blast plates and floodgates that would withstand rushing water in the case of an explosion.

But the MTA’s security makeover isn’t limited to tunnels. The agency’s seven bridges are being “hardened” with plates and “collars” on cables that can resist a blast, sources said.

The agency originally planned to use a lightweight, blast-resistant material to ring the tunnels — but sources said that various types of materials have been used.

One of more complicated tasks was determining which parts of the aged tunnels were bored deep into rock and which parts come close to the surface.

“That presents several issues. With some tunnels, there’s a point where they come out to the surface and there’s different vulnerability there than with tunnels in bedrock,” one source said.

In January, the state comptroller reported that “93 percent of all facility hardening was completed” and that the MTA’s project cost about $22 million more than expected.

“A lot has been done in regards to hardening, and that work continues to move forward,” said agency spokesman Kevin Ortiz.

The MTA’s security program also includes an increased police presence, and the “If You See Something, Say Something” campaign.